Dynamics of a globally modified magnetohydrodynamics equations with double delay.

Ngana, Aristide Ndongmo; Medjo, Theodore Tachim; Djomegni, Patrick Mimphis Tchepmo

In this paper, we study a globally modified system of Magnetohydrodynamics (MHD) equations in a three-dimensional domain, incorporating double delays in both the forcing and convective terms. The modification is made by means of cut-off functions that multiply the convective terms with delays of the equations, and this modification of the classical MHD equations results in more regular solutions, which depend continuously on the initial conditions and the parameters associated with the cut-off functions. Thus, we establish the existence and uniqueness of strong solutions, as well as the existence and uniqueness of pullback attractors for the modified system. Furthermore, using the generalized Banach limit argument, we construct a family of invariant Borel probability measures, which are supported on the pullback attractors.

INVARIANT measures; PROBABILITY measures; MAGNETOHYDRODYNAMICS; EQUATIONS; ARGUMENT

Communications on Pure & Applied Analysis, 2025, Vol 24, Issue 4, p1

1534-0392

Academic Journal

10.3934/cpaa.2025009